论惯性积平移和旋转变换的一般形式

给出了惯性积平移变换的一般关系式和旋转变换的一般关系式,由此可以解决一切惯性积的变换问题.     

Experimental and Real Coordinates in Space-Time Transformations

The experimental (apparent) space-time transformations connect coordinates altered by length contraction and clock retardation. When clocks are synchronized by means of light signals (Einstein–Poincaré procedure) or by slow clock transport, the experimental space-time. transformations assume the mathematical form of the Extended space-time transformations.⁽⁴⁾ These reduce to the Lorentz–Poincaré transformations when one of the frames they connect is the fundamental inertial frame. If the synchronization procedure were perfect, the experimental space-time transformations would assume the form of Selleris inertial transformations.⁽⁵⁾ The real space-time transformations are those which are disclosed when the systematic measurement distortions are corrected.     

POSSIBLE SPACE-TIME MANIFOLDS AND KINEMATICS

In this work, the analysis of the space-time manifolds, their kinematic groups and Lie algebras are made as intuitive as possible. First of all, an analysis ofthe inertial frames shows that the space-time manifold in which there exists a global inertial frame should be a pseudo-sphere so that the kinematic group must be a rotation group. Thus the explicit analytical expressions of such kinematical transformations and the commutation relations among the corresponding generators can be formulated easily. Consequently, the contractions of such manifolds,kinematic groups and Lie algebras can be deduced concretely and intuitively.     

A derivation of three-dimensional inertial transformations

The derivation of the transformations between inertial frames made by Mansouri and Sexl is generalised to three dimensions for an arbitrary direction of the velocity. Assuming length contraction and time dilation to have their relativistic values, a set of transformations kinematically equivalent to special relativity is obtained. The “clock hypothesis” allows the derivation to be extended to accelerated systems. A theory of inertial transformations maintaining absolute simultaneity is shown to be the only one logically consistent with accelerated movements. Algebraic properties of these transformations are discussed. Financial support from the Swiss National Science Foundation and the Swiss Academy of Engineering Sciences.     

Noninvariant one-way velocity of light

After discussing in the first five sections the meaning and the difficulties of the principle of relativity we present a new sel of spacetime transformations between inertial systems (inertial transformations), based on three assumptions: (1) The two-way velocity of light is c in all inertial systems and in all directions; (2) Time dilation effects take place with the usual relativistic factor; (3) Clocks are synchronized in the way chosen by nature itself, e.g., in the Sagnac effect. We show that our new transformation laws can explain the available experimental evidence in spite of the implied noninvariance of the one-way velocity of light.     

Consequences of the inertial equivalence of energy

The usual macroscopic theory of relativistic mechanics and electromagnetism is formulated so that all assumptions but one are consistent with both special relativity and Newtonian mechanics, the distinguishing assumption being that to any energyE, whatever its form, there corresponds an inertial massE/c ² . The speed of light enters this formulation only as a consequence of the inertial equivalent of energy1/c ² . While, for1/c ² >0 the resulting theory has symmetry under the Poincaré group, including Lorentz transformations, all its physical consequences can be derived and tested in any one inertial frame. In particular, an account is given in one inertial frame for the dynamic causes of relativistic effects for simple accelerated clocks and roads.     

On the transformation of mass and momentum densities in special relativity

By considering the mass and momentum densities of a point mass moving at uniform velocity, the known transformation of these densities from a representation in one inertial system to another is easily derived. The transformation is not linear in mass and momentum density, but the introduction of a dyadic stress density tensor gives a linear relation. The transformation is shown to hold for a general continuous mass distribution in which mass and momentum are conserved, provided a specific choice is made for the stress density tensor. This result contrasts with the particle viewpoint of matter in which only the divergence of the stress density tensor need be fixed so far as the transformation is concerned. A change of functions is made which greatly simplifies the transformations. The new functions are shown to represent a conserved fluid.Research supported in part by a grant from the California State University, Long Beach Foundation.     

Note on Clock Synchronization and Edwards Transformations

Edwards transformations relating inertial frames with arbitrary clock synchronization are reviewed and put in more general setting. Their group-theoretical context is described.     

A Universal Regulator?

By using the principle of metrical invariance which requires that all physical laws are independent of the choice of units (alternatively, all physical laws are invariant with respect to scale transformations of space-time coordinates) and Goldstone's theorem, a universal regulator is discovered. The cosmic field is the Yang-Mills field of the local scale transformations. Its physical role is as follows. Cosmon, its quantum, is a massless, spinless, and neutral particle. The cosmic field is created by inertial masses. Therefore it participates in all physical processes and if its presence is taken into account, then the quantum field theory is free from all ultraviolet infinities. From the point of view of Yang-Mills field theory, it is proved that the so-called gravitational masses are identical with inertial masses and the gravitational field is created by inertial masses moving non-inertially. This fact permits to solve satisfactorily the problem of energy-momentum complex of the gravitational field. The system of equations which defines simultaneously the cosmic and gravitational fields is established. A non-Einstein cosmology is outlined.     

Invariance Properties of the Entropy Production,and the Entropic Pairing of Inertial Frames of Reference by Shear-Flow Systems

This study examines the invariance properties of the thermodynamic entropy production in its global (integral), local (differential), bilinear, and macroscopic formulations, including dimensional scaling, invariance to fixed displacements, rotations or reflections of the coordinates, time antisymmetry, Galilean invariance, and Lie point symmetry. The Lie invariance is shown to be the most general, encompassing the other invariances. In a shear-flow system involving fluid flow relative to a solid boundary at steady state, the Galilean invariance property is then shown to preference a unique pair of inertial frames of reference—here termed an entropic pair—respectively moving with the solid or the mean fluid flow. This challenges the Newtonian viewpoint that all inertial frames of reference are equivalent. Furthermore, the existence of a shear flow subsystem with an entropic pair different to that of the surrounding system, or a subsystem with one or more changing entropic pair(s), requires a source of negentropy—a power source scaled by an absolute temperature—to drive the subsystem. Through the analysis of different shear flow subsystems, we present a series of governing principles to describe their entropic pairing properties and sources of negentropy. These are unaffected by Galilean transformations, and so can be understood to “lie above” the Galilean inertial framework of Newtonian mechanics. The analyses provide a new perspective into the field of entropic mechanics, the study of the relative motions of objects with friction.     

The introduction of Superluminal Lorentz transformations: A revisitation

We revisit the introduction of the Superluminal Lorentz transformations which carry from bradyonic inertial frames to tachyonic inertial frames, i.e., which transform time-like objects into space-like objects, andvice versa. It has long been known that special relativity can be extended to Superluminal observers only by increasing the number of dimensions of the space-time or—which is in a sense equivalent—by releasing the reality condition (i.e., introducing also imaginary quantities). In the past we always adopted the latter procedure. Here we show the connection between that procedure and the former one. In other words, in order to clarify the physical meaning of the imaginary units entering the classical theory of tachyons, we have temporarily to call into play anauxiliary six-dimensional space-time M(3, 3); however, we are eventually able to go back to the four-dimensional Minkowski space-time. We revisit the introduction of the Superluminal Lorentz transformations also under another aspect. In fact, the generalized Lorentz transformations had been previously written down in a form suited only for the simple case of collinear boosts (e.g., they formed a group just for collinear boosts). We express now the Superluminal Lorentz transformations in a more general form, so that they constitute a group together with the ordinary—orthochronousand antichronous—Lorentz transformations, and reduce to the previous form in the case of collinear boosts. Our approach introduces either real or imaginary quantities, with exclusion of (generic) complex quantities. In the present context, a procedure—in two steps—for interpreting the imaginary quantities is put forth and discussed. In the case of a chain of generalized Lorentz transformations, such a procedure (when necessary) is to be applied only at the end of the chain. Finally, we justify why we call transformations also the Superluminal ones.     

Relativistic aberrations in quantum phase space

A phase space treatment of special relativity of quantum systems is developed. In this approach a quantum particle remains localized if subject to inertial transformations, the localization occurring in a finite phase space area. Unlike in the non-relativistic case, relativistic transformations generally distort the phase space distribution function, being equivalent to aberrations in optics. The relativistic aberrations of massive particles are in general different from those of optical images.     

Do experiments imply special relativity?

Starting with a thorough and self-contained account of transformations between inertial observers, the most general frame transformation is derived, which fully incorporates the Michelson-Morley experiment and the transverse Doppler effect. Lorentz and Marinov transformations are presented as two particular cases. On a rigorous mathematical ground, the paper presents a theory, more general than special relativity and with three degrees of freedom, that completely agrees with a well-established phenomenology.     

Non-lorentz transformations of reference systems

The structure of transformations is investigated which describe the transition from an inertial reference system to a noninertial one and conversely. As a result of such transition the curvature of the space of events is modified, and one is thus able to discuss its observational character. This leads to a new interpretation of the general relativity theory in which the space curvature is now related only to the noninertial motion of the observer. Transition from a noninertial reference system corresponding to the Schwarzschild space to an inertial reference system (plane space) is considered as an example.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 104–112, May, 1973.     

The application of special relativity to the right-angled lever

The Lorentz transformation relates the Einstein-defined measures, associated with two inertial frames, of the space and time coordinates of a body or event. From such information relative velocities and accelerations may be deduced, and their appropriate transformations derived. All other transformations of special relativity are derived from the Lorentz transformation and hence depend on the coordinate measures related by the transformation. In particular, the transformation of forces depends on that for accelerations; hence it may not be appropriately applicable to equilibrium phenomena involving null-acceleration. It is suggested that this is the root of the apparent paradox which arises when the conventional force transformation is applied to the consideration of a right-angled lever in equilibrium in its proper inertial frame. It is shown that this paradox is resolved by the employment of a nonconventional but appropriate special relativistic transformation for forces not associated with corresponding accelerations.     

Use of the Lorentz Transformations in Noninertial Reference Frames

The Lorentz transformations are used within the model of a noninertial reference frame without infinitely high accelerations arising at instantaneous jumps of an accelerated observer between different inertial reference frames. It is demonstrated that the twin paradox can be explained within this model with the help of the Lorentz transformations. Based on the model of a noninertial reference frame, the acceleration a measured in the noninertial reference frame is related to the acceleration a measured in an inertial reference frame.     

Reciprocal Relativity of Noninertial Frames and the Quaplectic Group

The frame associated with a classical point particle is generally noninertial. The point particle may have a nonzero velocity and force with respect to an absolute inertial rest frame. In time–position–energy–momentum-space {t, q, p, e}, the group of transformations between these frames leaves invariant the symplectic metric and the classical line element ds² = d t². Special relativity transforms between inertial frames for which the rate of change of momentum is negligible and eliminates the absolute rest frame by making velocities relative but still requires the absolute inertial frame. The Lorentz group leaves invariant the symplectic metric and the line elements and . General relativity for particles under only the influence of gravity avoids the issue of noninertial frames as all particles follow geodesics and hence have locally inertial frames. For other forces, the question of the absolute inertial frame remains.) Born conjectured that the line element should be generalized to the pseudo-orthogonal metric . The group leaving this metrics and the symplectic metric invariant is the pseudo-unitary group of transformations between noninertial frames. We show that these transformations also eliminate the need for an absolute inertial frame by making forces relative and bounded by b and so embodies a relativity that is shape reciprocal in the sense of Born. The inhomogeneous version of this group is naturally the semidirect product of the pseudo-unitary group with the nonabelian Heisenberg group. This is the quaplectic group.     

Multiple-step martensitic transformations in Ni-rich NiTi alloys--an in-situ transmission electron microscopy investigation

Multiple-step martensitic transformations in Ni-rich NiTi shape memory alloys have so far been rationalized on the basis of dislocation stress fields, coherency stress fields around Ni 4 Ti 3 precipitates and evolving Ni concentrations between precipitates during ageing. The primary objective of the present paper is to show that such transformations can also occur owing to heterogeneous microstructures that form during ageing of solution annealed defect-free materials. These microstructures are characterized by Ni 4 Ti 3 grain-boundary precipitation and by precipitate-free grain interiors. Two microstructures which give rise to two and three distinct differential scanning calorimetry (DSC) peaks on cooling from the B2 regime are subjected to in-situ cooling and heating cycles in the transmission electron microscope. Martensitic transformations are directly studied and the observations provide a new explanation for multiple-step martensitic transformations in Ni-rich NiTi alloys. Most importantly the results of the present study allow us to understand why DSC chart features on cooling from the B2 regime change during ageing, where they lose their one-step character (after solution annealing at 1123 K for 900 s) and evolve from two-step (after ageing at 773 K for 3.6 ks) to three-step (after ageing at 773 for 36 ks K) transformations.